On Derivations of the Uncertainty Principle

Robert Yaris

N. K. Tyagi

Steeve Zozor, M. Portesi, Christophe Vignat

Feifei Qu

Abstract The classical uncertainty principle works for smooth signal functions. In our work, we apply the Fourier transform derivatives for the study of uncertainty principle, so that the smoothness condition for the signal functions is not required. At first, the amplitude and phase derivatives of vector-valued signal functions based on the Fourier transform are defined. Then we obtain a strong form of the uncertainty principle.

Jan Hilgevoord, Jos Uffink

Hugo Weichel

The uncertainty principle is used to derive the ultimate spectral width of the laser beam. The resulting expression is the Schawlow–Townes formula. The derivation is simple and can readily be incorporated into an introductory course on lasers. The derivation can also be used in a modern physics course to illustrate the usefulness of the uncertainty principle.